Magnetic breakdown phenomena have been investigated in the longitudinal magnetoresistance of the quasi-two-dimensional (Q2D) superconductor kappa-(BEDT-TTF)(2)Cu(NCS)(2) in magnetic fields of up to 50 T, well above the characteristic breakdown field. The material is of great interest because its relatively simple Fermi surface, consisting of a closed Q2D pocket and an open Q1D band, is almost identical to the initial hypothetical breakdown network proposed by Pippard. Two frequencies are expected to dominate the magnetoresistance oscillations: the a frequency, corresponding to orbits around the closed pocket, and the beta frequency, corresponding to the simplest classical breakdown orbit. However, a beta - alpha frequency is in fact found to be the dominant high-frequency oscillation in the magnetoresistance. Numerical simulations, employing standard theories for calculating the density of states, indicate that a significant presence of the beta - alpha frequency (forbidden in the standard theories) can result simply from the frequency-mixing effects associated with the pinning of the chemical potential in a quasi-two-dimensional system. While this effect is able to account for the previous experimental observation of beta - alpha frequency oscillations of small amplitude in the magnetization, it cannot explain why such a frequency dominates the high-field magnetotransport spectrum. Instead we have extended the numerical simulations to include a quantum interference model adapted for longitudinal magnetoresistance in a quasi-two-dimensional conductor. The modified simulations are then able to account for most of the features of the experimental magnetoresistance data.